Coherence

K. D. Möller

Hai‐Bo Xing, Ming Yang

We discuss the coherence-assisted transformation of pure coherent states under incoherent operations and show that the amount of coherence loss can be reduced with the help of the auxiliary coherent state. Starting with the simplest case i.e., the main coherent state and auxiliary coherent state are both 2×2 dimensional, we compare the change of coherence before and after the transformation and find that the amount of coherence loss can be reduced due to the increase of the coherence of auxiliary coherent state. In general, when the main coherent state and auxiliary coherent state are high-dimensional, the result is also true. For the coherence of auxiliary coherent state is increased, we can get the maximally coherent state at some conditions, this case can be viewed as a new way for the distillation of coherent state. These interesting results of coherence transformation will give us a better understanding of the resource manipulation.

Vyacheslav I. Yukalov

The basic notions related to coherence phenomena are formulated. Two types of coherence are described, state coherence and transition coherence. Useful characteristics for quantifying coherence are defined, such as coherence functions, coherence radius, coherence length, and coherence time.

Karl D. Möller, Claude Bélorgoet

Deng-hui Yu, Li‐qiang Zhang, Chang‐shui Yu

Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational meaning. We show that any state can be produced from some input pure states via the corresponding incoherent channels. It is found that the coherence of a given state can be well characterized by the least coherence of the input pure states, so a coherence monotone is established by only effectively quantifying the input pure states. In particular, we show that our proposed coherence monotone is the supremum of all the coherence monotones that give the same coherence for any given pure state. We also prove that our coherence monotone is continuous. Considering the convexity, we prove that our proposed coherence measure is a subset of the coherence measure based on the convex roof construction. The similarities and differences between our coherence monotone and coherence cost are studied in detail. As applications, we give a concrete expression of our coherence measure by employing the geometric coherence of a pure state. We also give a thorough analysis of the states of the qubit and finally obtain a series of analytic coherence measures. The numerical examples are also given to show the difference between our coherence monotone and that based on the convex roof construction.